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# torch.fft.hfft2¶

torch.fft.hfft2(input, s=None, dim=(- 2, - 1), norm=None, *, out=None)

Computes the 2-dimensional discrete Fourier transform of a Hermitian symmetric input signal. Equivalent to hfftn() but only transforms the last two dimensions by default.

input is interpreted as a one-sided Hermitian signal in the time domain. By the Hermitian property, the Fourier transform will be real-valued.

Note

Supports torch.half and torch.chalf on CUDA with GPU Architecture SM53 or greater. However it only supports powers of 2 signal length in every transformed dimensions. With default arguments, the size of last dimension should be (2^n + 1) as argument s defaults to even output size = 2 * (last_dim_size - 1)

Parameters:
• input (Tensor) – the input tensor

• s (Tuple[int], optional) – Signal size in the transformed dimensions. If given, each dimension dim[i] will either be zero-padded or trimmed to the length s[i] before computing the Hermitian FFT. If a length -1 is specified, no padding is done in that dimension. Defaults to even output in the last dimension: s[-1] = 2*(input.size(dim[-1]) - 1).

• dim (Tuple[int], optional) – Dimensions to be transformed. The last dimension must be the half-Hermitian compressed dimension. Default: last two dimensions.

• norm (str, optional) –

Normalization mode. For the forward transform (hfft2()), these correspond to:

• "forward" - normalize by 1/n

• "backward" - no normalization

• "ortho" - normalize by 1/sqrt(n) (making the Hermitian FFT orthonormal)

Where n = prod(s) is the logical FFT size. Calling the backward transform (ihfft2()) with the same normalization mode will apply an overall normalization of 1/n between the two transforms. This is required to make ihfft2() the exact inverse.

Default is "backward" (no normalization).

Keyword Arguments:

out (Tensor, optional) – the output tensor.

Example

Starting from a real frequency-space signal, we can generate a Hermitian-symmetric time-domain signal: >>> T = torch.rand(10, 9) >>> t = torch.fft.ihfft2(T)

Without specifying the output length to hfftn(), the output will not round-trip properly because the input is odd-length in the last dimension:

>>> torch.fft.hfft2(t).size()
torch.Size([10, 10])


So, it is recommended to always pass the signal shape s.

>>> roundtrip = torch.fft.hfft2(t, T.size())
>>> roundtrip.size()
torch.Size([10, 9])
>>> torch.allclose(roundtrip, T)
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